.TH  DLANSF 1 "November 2008" " LAPACK routine (version 3.2)                                    " " LAPACK routine (version 3.2)                                    " 
.SH NAME
DLANSF - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A in RFP format
.SH SYNOPSIS
.TP 17
DOUBLE PRECISION
FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK )
.TP 17
.ti +4
CHARACTER
NORM, TRANSR, UPLO
.TP 17
.ti +4
INTEGER
N
.TP 17
.ti +4
DOUBLE
PRECISION A( 0: * ), WORK( 0: * )
.SH PURPOSE
DLANSF returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
real symmetric matrix A in RFP format.
.SH DESCRIPTION
DLANSF returns the value
.br
   DLANSF = ( max(abs(A(i,j))), NORM = \(aqM\(aq or \(aqm\(aq
.br
            (
.br
            ( norm1(A),         NORM = \(aq1\(aq, \(aqO\(aq or \(aqo\(aq
.br
            (
.br
            ( normI(A),         NORM = \(aqI\(aq or \(aqi\(aq
.br
            (
.br
            ( normF(A),         NORM = \(aqF\(aq, \(aqf\(aq, \(aqE\(aq or \(aqe\(aq
where  norm1  denotes the  one norm of a matrix (maximum column sum),
normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
normF  denotes the  Frobenius norm of a matrix (square root of sum of
squares).  Note that  max(abs(A(i,j)))  is not a  matrix norm.
.SH ARGUMENTS
.TP 8
NORM    (input) CHARACTER
Specifies the value to be returned in DLANSF as described
above.
.TP 8
TRANSR  (input) CHARACTER
Specifies whether the RFP format of A is normal or
transposed format.
= \(aqN\(aq:  RFP format is Normal;
.br
= \(aqT\(aq:  RFP format is Transpose.
.TP 8
UPLO    (input) CHARACTER
On entry, UPLO specifies whether the RFP matrix A came from
an upper or lower triangular matrix as follows:
.br
= \(aqU\(aq: RFP A came from an upper triangular matrix;
.br
= \(aqL\(aq: RFP A came from a lower triangular matrix.
.TP 8
N       (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, DLANSF is
set to zero.
.TP 8
A       (input) DOUBLE PRECISION array, dimension ( N*(N+1)/2 );
On entry, the upper (if UPLO = \(aqU\(aq) or lower (if UPLO = \(aqL\(aq)
part of the symmetric matrix A stored in RFP format. See the
"Notes" below for more details.
Unchanged on exit.
.TP 8
WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = \(aqI\(aq or \(aq1\(aq or \(aqO\(aq; otherwise,
WORK is not referenced.
.SH FURTHER DETAILS
We first consider Rectangular Full Packed (RFP) Format when N is
even. We give an example where N = 6.
.br
    AP is Upper             AP is Lower
.br
 00 01 02 03 04 05       00
.br
    11 12 13 14 15       10 11
.br
       22 23 24 25       20 21 22
.br
          33 34 35       30 31 32 33
.br
             44 45       40 41 42 43 44
.br
                55       50 51 52 53 54 55
.br
Let TRANSR = \(aqN\(aq. RFP holds AP as follows:
.br
For UPLO = \(aqU\(aq the upper trapezoid A(0:5,0:2) consists of the last
three columns of AP upper. The lower triangle A(4:6,0:2) consists of
the transpose of the first three columns of AP upper.
.br
For UPLO = \(aqL\(aq the lower trapezoid A(1:6,0:2) consists of the first
three columns of AP lower. The upper triangle A(0:2,0:2) consists of
the transpose of the last three columns of AP lower.
.br
This covers the case N even and TRANSR = \(aqN\(aq.
.br
       RFP A                   RFP A
.br
      03 04 05                33 43 53
.br
      13 14 15                00 44 54
.br
      23 24 25                10 11 55
.br
      33 34 35                20 21 22
.br
      00 44 45                30 31 32
.br
      01 11 55                40 41 42
.br
      02 12 22                50 51 52
.br
Now let TRANSR = \(aqT\(aq. RFP A in both UPLO cases is just the
transpose of RFP A above. One therefore gets:
.br
         RFP A                   RFP A
.br
   03 13 23 33 00 01 02    33 00 10 20 30 40 50
.br
   04 14 24 34 44 11 12    43 44 11 21 31 41 51
.br
   05 15 25 35 45 55 22    53 54 55 22 32 42 52
.br
We first consider Rectangular Full Packed (RFP) Format when N is
odd. We give an example where N = 5.
.br
   AP is Upper                 AP is Lower
.br
 00 01 02 03 04              00
.br
    11 12 13 14              10 11
.br
       22 23 24              20 21 22
.br
          33 34              30 31 32 33
.br
             44              40 41 42 43 44
.br
Let TRANSR = \(aqN\(aq. RFP holds AP as follows:
.br
For UPLO = \(aqU\(aq the upper trapezoid A(0:4,0:2) consists of the last
three columns of AP upper. The lower triangle A(3:4,0:1) consists of
the transpose of the first two columns of AP upper.
.br
For UPLO = \(aqL\(aq the lower trapezoid A(0:4,0:2) consists of the first
three columns of AP lower. The upper triangle A(0:1,1:2) consists of
the transpose of the last two columns of AP lower.
.br
This covers the case N odd and TRANSR = \(aqN\(aq.
.br
       RFP A                   RFP A
.br
      02 03 04                00 33 43
.br
      12 13 14                10 11 44
.br
      22 23 24                20 21 22
.br
      00 33 34                30 31 32
.br
      01 11 44                40 41 42
.br
Now let TRANSR = \(aqT\(aq. RFP A in both UPLO cases is just the
transpose of RFP A above. One therefore gets:
.br
         RFP A                   RFP A
.br
   02 12 22 00 01             00 10 20 30 40 50
.br
   03 13 23 33 11             33 11 21 31 41 51
.br
   04 14 24 34 44             43 44 22 32 42 52
.br
Reference
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=========
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